Interview Q&A / Aptitude

31. Early one morning Priya is standing in an open field, and her shadow falls exactly to her right. Which direction is she facing?

    South. In the morning the sun is in the east, so shadows fall towards the west. If west is on her right, she must be facing south.

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32. Find the wrong term in the series 3, 7, 15, 27, 63, 127.

    27 is wrong; it should be 31. Each term is double the previous plus 1: 3, 7, 15, 31, 63, 127. Equivalently each term is 2^n - 1.

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33. Five friends A, B, C, D and E sit in a row facing north. C is in the middle, A is at the right end, B sits immediately to the left of C, and E is not at either end. Who sits between A and C, and who is at the left end?

    E sits between A and C, and D is at the left end. Numbering seats 1 to 5 from the left: C = 3, A = 5, B = 2, so D and E take 1 and 4, and since E is not at an end, E = 4 and D = 1. The order is D, B, C, E, A.

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34. Four bells toll at intervals of 6, 8, 12 and 18 minutes. If they toll together at 8:00 AM, when do they next toll together, and how many times in 12 hours?

    LCM(6, 8, 12, 18) = 72 minutes, so they next ring together at 9:12 AM. In 12 hours (720 minutes) they ring together 720 / 72 = 10 more times, or 11 times counting the 8:00 AM ring.

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35. How do you convert odds in favour or odds against into a probability?

    Odds in favour a : b means a favourable outcomes for every b unfavourable, so the probability is a/(a + b). Odds against a : b mean probability b/(a + b). Odds in favour 3 : 5 give P = 3/8; odds against 7 : 3 give P = 3/10.

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36. How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition?

    300. The first digit cannot be 0, so it has 5 choices. The remaining three places use the other 5 digits: 5 x 4 x 3. Total = 5 x 5 x 4 x 3 = 300.

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37. How many times in a day do the hands of a clock coincide, and how many times are they at right angles?

    They coincide 22 times in 24 hours (11 times every 12 hours, since the coincidence between 11 and 1 happens only once, at 12). They are at right angles 44 times a day and opposite each other 22 times.

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38. How many trailing zeros does 250! have?

    62. Each trailing zero needs a pair of 2 and 5, and 5s are scarcer, so count the 5s: 250/5 = 50, 250/25 = 10, 250/125 = 2 (take whole parts), total 62.

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39. If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?

    8 : 12 : 15. Make the common term B equal in both ratios. B is 3 in the first and 4 in the second, so scale the first by 4 and the second by 3: A : B = 8 : 12 and B : C = 12 : 15.

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40. If A's salary is 20% more than B's, by what percentage is B's salary less than A's?

    B's salary is 16.67% (1/6) less than A's. If B earns 100, A earns 120. The gap of 20 is measured against A's 120: 20/120 = 1/6 = 16.67%.

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41. If COMPUTER is coded as DPNQVUFS, how is SYSTEM coded in the same language?

    TZTUFN. Each letter of COMPUTER is shifted one place forward (C to D, O to P, and so on), so SYSTEM becomes T, Z, T, U, F, N.

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42. If the cost price of 20 articles equals the selling price of 16 articles, what is the profit or loss percentage?

    A profit of 25%. Let each article cost ₹1. Then 16 articles sell for ₹20, so one sells for ₹1.25, a profit of 25%. Formula: (20 - 16)/16 x 100 = 25%.

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43. If the price of sugar rises by 25%, by what percentage must a family cut its consumption to keep its spending the same?

    By 20%. Spending = price x quantity. If price becomes 125/100 of the old price, quantity must become 100/125 = 4/5, a cut of 1/5, which is 20%. Formula: r / (100 + r) x 100 = 25/125 x 100 = 20%.

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44. In a row of 40 students, Rahul is 12th from the left. Neha is 4th to the right of Rahul. What is Neha's position from the right end?

    25th from the right. Neha is 12 + 4 = 16th from the left. Position from the right = total - position from the left + 1 = 40 - 16 + 1 = 25.

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45. In an election between two candidates, 20% of the 8,000 votes cast were invalid. The winner got 55% of the valid votes. How many valid votes did the loser get?

    2,880. Valid votes = 80% of 8,000 = 6,400. The loser got 100% - 55% = 45% of valid votes: 0.45 x 6,400 = 2,880. The winning margin is 10% of 6,400 = 640.

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46. In how many distinct ways can the letters of the word BANANA be arranged?

    60. BANANA has 6 letters with A repeated 3 times and N repeated 2 times, so the count is 6! / (3! x 2!) = 720 / 12 = 60.

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47. In what ratio should rice costing ₹40 per kg be mixed with rice costing ₹55 per kg to get a mixture worth ₹45 per kg?

    2 : 1. By alligation, cheaper : dearer = (55 - 45) : (45 - 40) = 10 : 5 = 2 : 1. Check: 2 kg at ₹40 plus 1 kg at ₹55 costs ₹135 for 3 kg, which is ₹45 per kg.

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48. Pipes A and B fill a tank in 12 and 15 minutes. Pipe C empties it in 20 minutes. If all three are opened together on an empty tank, how long will it take to fill?

    10 minutes. With 60 units of tank: A adds 5, B adds 4, C removes 3 per minute. Net 6 units per minute, so 60/6 = 10 minutes.

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49. Pointing to a photograph of a man, Arjun says, 'He is the son of the only son of my grandfather.' How is the man related to Arjun?

    He is Arjun's brother. The only son of Arjun's (paternal) grandfather is Arjun's father, and a son of Arjun's father who is someone other than Arjun is Arjun's brother.

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50. Ravi walks 10 km north, turns right and walks 6 km, then turns right again and walks 18 km. How far is he from his starting point, and in which direction?

    10 km to the south-east. After the moves he is 6 km east and 10 - 18 = 8 km south of the start. Distance = square root of (6^2 + 8^2) = 10 km.

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51. Rohan's age 6 years from now will be 5/3 of his age 6 years ago. What is his present age?

    24 years. If his age is x, then x + 6 = (5/3)(x - 6). So 3x + 18 = 5x - 30, giving x = 24. Check: 30 is 5/3 of 18.

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52. Section A has 30 students with an average of 60 marks and Section B has 20 students with an average of 70. What is the combined average?

    64. Use a weighted average: (30 x 60 + 20 x 70) / 50 = (1,800 + 1,400) / 50 = 3,200 / 50 = 64. It is not 65, because the larger section pulls the average towards 60.

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53. Statements: All cats are dogs. No dog is a rat. Conclusions: I. No cat is a rat. II. Some rats are cats. Which conclusions follow?

    Only I follows. Every cat is inside the dogs circle, and the dogs circle shares nothing with rats, so no cat can be a rat. II contradicts I, so it cannot follow.

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54. Statements: All pens are books. Some books are bags. Conclusions: I. Some pens are bags. II. Some bags are books. Which conclusions follow?

    Only II follows. 'Some books are bags' can be reversed to 'some bags are books', so II is certain. I is not certain: the books that are bags might be entirely outside the pens, so pens and bags need not overlap.

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55. The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. What is the sixth result?

    56. The first six and the last six together count the sixth result twice: 6 x 49 + 6 x 52 = 294 + 312 = 606, while all 11 total 550. The extra 56 is the sixth result.

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56. The average weight of 30 students is 40 kg. When the teacher's weight is included, the average rises by 1 kg. What is the teacher's weight?

    71 kg. New total = 31 x 41 = 1,271 kg; old total = 30 x 40 = 1,200 kg. Teacher = 71 kg. Shortcut: 41 (the new average) + 30 x 1 (raising each student by 1) = 71.

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57. The HCF of two numbers is 12 and their LCM is 336. If one number is 48, what is the other?

    The other number is 84. For any two numbers, HCF x LCM = product of the numbers, so the other number is 12 x 336 / 48 = 84.

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58. The sum of the ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?

    4 years. If the youngest is x, the others are x + 3, x + 6, x + 9 and x + 12. So 5x + 30 = 50 and x = 4. The ages are 4, 7, 10, 13 and 16.

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59. Two numbers are in the ratio 3 : 5. If 9 is added to each, the ratio becomes 3 : 4. Find the numbers.

    9 and 15. Let them be 3x and 5x. Then (3x + 9)/(5x + 9) = 3/4, so 12x + 36 = 15x + 27, giving x = 3. The numbers are 9 and 15, and 18 : 24 is indeed 3 : 4.

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60. Two vessels contain milk and water in the ratios 3 : 1 and 5 : 3. If equal quantities from both are mixed, what is the ratio of milk to water?

    11 : 5. Milk fractions are 3/4 and 5/8. Taking one litre from each gives milk 3/4 + 5/8 = 11/8 litres out of 2, so milk is 11/16 and water 5/16 of the mixture.

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